中国物理B ›› 2004, Vol. 13 ›› Issue (9): 1386-1390.doi: 10.1088/1009-1963/13/9/003

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Physical mechanism of the chaotic detection of the unknown frequency of weak harmonic signal and effects of damping ratio on the detection results

杨宝俊1, 李月2, 邓小英2, 金雷2, 杜立志2   

  1. (1)Department of Geophysics, Jilin University, Changchun 130026, China; (2)Department of Information Engineering, Jilin University, Changchun 130012, China
  • 收稿日期:2004-01-14 修回日期:2004-05-10 出版日期:2004-06-21 发布日期:2005-06-21
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 40374045).

Physical mechanism of the chaotic detection of the unknown frequency of weak harmonic signal and effects of damping ratio on the detection results

Li Yue (李月)a, Yang Bao-Jun (杨宝俊)b, Deng Xiao-Ying (邓小英)a, Jin Lei (金雷)a, Du Li-Zhi (杜立志)a   

  1. a Department of Information Engineering, Jilin University, Changchun 130012, China; b Department of Geophysics, Jilin University, Changchun 130026, China
  • Received:2004-01-14 Revised:2004-05-10 Online:2004-06-21 Published:2005-06-21
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 40374045).

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摘要： In the zero-order approximation, we use the perturbation method of parameter with small magnitude to prove that the harmonic frequency in the solution of the equation is close to that of the driving force when the chaotic system from Duffing－Holmes equation stays in the stable periodic state, which is the physical mechanism of the detection of the unknown frequency of weak harmonic signal using the chaotic theory. The result of the simulation experiment shows that the method proposed in this paper, by which one can determine the frequency of the stable system from the number of circulation change of the phase state directionally across a fixed phase state point (x,\dot{x}) in fixed simulation time period, is successful. Analyzing the effects of the damping ratio on the chaotic detection result, one can see that for different frequency ranges it is necessary to carefully choose corresponding damping ratio α.

关键词: weak harmonic signal, unknown frequency, chaotic detection, damping ratio

Abstract: In the zero-order approximation, we use the perturbation method of parameter with small magnitude to prove that the harmonic frequency in the solution of the equation is close to that of the driving force when the chaotic system from Duffing－Holmes equation stays in the stable periodic state, which is the physical mechanism of the detection of the unknown frequency of weak harmonic signal using the chaotic theory. The result of the simulation experiment shows that the method proposed in this paper, by which one can determine the frequency of the stable system from the number of circulation change of the phase state directionally across a fixed phase state point ($x,\dot{x}$) in fixed simulation time period, is successful. Analyzing the effects of the damping ratio on the chaotic detection result, one can see that for different frequency ranges it is necessary to carefully choose corresponding damping ratio $\alpha$.

Key words: weak harmonic signal, unknown frequency, chaotic detection, damping ratio

中图分类号:  (Numerical simulations of chaotic systems)

  • 05.45.Pq
05.45.Gg (Control of chaos, applications of chaos)